1. Technical Field
The present invention relates to a method of making measurements in three-dimensions using the chromatic dispersion of a diffraction grating.
2. Related Art
Diffraction range finders are devices which determine distance by correlating the relationship between the distances of a diffraction grating from an illuminated target surface with the respective relative displacements of high-order diffraction images from the position of the respective zero-order image as observed through the diffraction grating. The target must be self-illuminated or illuminated by a secondary source of energy propagated by periodic waves. Higher-order diffraction images of a target are reconstructed at a receiver which has a means to focus the radiation onto a transducer that can sense the position of the higher-order diffraction images. As a target is moved toward or away from a grating surface, the relative displacement of a higher-order image from both the zero-order image and other higher-orders images can be measured to take target range.
Chromatic dispersion has previously been used within structured illumination projectors to light a surface being ranged through a triangulation or parallax method.
The xe2x80x9cRainbow Range Finderxe2x80x9d and its principles of operation are discussed U.S. Pat. Nos. 4,864,395; 5,200,792; and 5,157,487. Zheng Jason Geng holds U.S. Pat. Nos. 5,675,407; 6,028,672; and 6,147,760 for related inventions.
Rainbow range finders take range readings by projection of a pattern of colors onto a target and then taking the further step of correlating the colors on the target with the distances to a receiver that can discriminate the colors. All published embodiments of rainbow range finder presume a structured illumination source that projects a pattern of unique color hues onto a target surface. Typically, a rainbow projector will have a diffraction grating inside the projector that coverts the radiation from an incandescent light bulb into a broad spectrum. Said spectrum is then focused onto a target surface. The receiver can be an ordinary color video camera that has separate sensors for red, green and blue, as is typical of most television cameras. As asserted in these patents, there are well understood techniques of colorimetry for making determinations of a unique color at each pixel site in the camera by measuring the relative intensity of the primary colors. The present inventor has demonstrated such a method for such color discrimination using television cameras with red, green and blue channels (xe2x80x9cPantomationxe2x80x94A System for Position Tracking,xe2x80x9d Tom DeWitt and Phil Edelstein, Proceedings of the Second Symposium on Small Computers in the Arts, 1982, IEEE Computer Society, No. 455, pp. 61-70).
The Rainbow Range Finder relies on triangulation to make range measurements and therefore suffers from the intrinsic limitations of a parallax-based range finder. Among these limitations are perspective foreshortening which results in an inverse square relationship of accuracy to distance. Triangulation also suffers from the liability that occluded regions can occur between the projector and receiver causing obscured regions devoid of readings. Furthermore, as applied to profilometry, all triangulation devices make a trade-off between target height and depth sensitivity.
The limitations endemic to triangulation ranging methods as found, for example, in the Rainbow Range Finder led to the development of an improved method of range finding that uses a diffraction grating in the receiver.
Patents that teach how a range finder can be made with diffraction gratings are:
U.S. Pat. No. 4,678,324 awarded to Tom DeWitt (now known as Tom Ditto, the inventor of the present invention) on Jul. 7, 1987 for xe2x80x9cRange Finding by Diffraction.xe2x80x9d
U.S. Pat. No. 5,076,698 granted to Smith et al. on Dec. 31, 1991 for xe2x80x9cSensing the Shape of an Object.xe2x80x9d
PCT/US1997/02384, priority date Dec. 30, 1996, laid open as WIPO WO1999/044013 and published as Canadian Patent Application CA2277211, xe2x80x9cVARIABLE PITCH GRATING FOR DIFFRACTION RANGE FINDING SYSTEM,xe2x80x9d inventors Ditto and Lyon.
The ""324 patent supra teaches xe2x80x9cIt has been found that the objects of the present invention may be realized by projecting a monochromatic pencil beam of light at a target, viewing the illuminated target through a diffraction grating, and measuring the displacement of the higher order diffraction images from the position of the zero order image lines,xe2x80x9d [column 4, lines 56-61].
In FIG. 1, adapted from Thomas D. DeWitt and Douglas A. Lyon, xe2x80x9cA Range Finding Method Using Diffraction Gratings,xe2x80x9d Applied Optics, May 10, 1995, Vol. 34 No. 14, pp. 2510-2521, the authors describe a mathematical relationship in the diffraction range finder whereby range can be determined by measuring the displacement x 104 of a higher-order diffraction image formed at the focal plane of a camera 130. The displacement x 104 is measured with respect to point 107 located at the center of the focal plane of the camera 130. The distance D 100 from the target 150 to grating 120 can be measured along a line of light from a laser 110. The relationships of a diffraction range finder be described geometrically as:                     D        =                                            (                                                                    1                    -                                                                  (                                                                              n                            ⁢                                                          λ                              p                                                                                -                                                      sin                            ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                              ρ                                +                                                                  arctan                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                          x                                      F                                                                        )                                                                                                                              )                                                                                                      )                                            2                                                                                                            n                    ⁢                                          λ                      p                                                        -                                      sin                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              ρ                        +                                                  arctan                          ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                          x                              F                                                        )                                                                                              )                                                                                  )                        ⁢                          xe2x80x83                        ⁢                          (                                                d                  ⁢                                      xe2x80x83                                    ⁢                  tan                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          ρ                      +                                              arctan                        ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                      x                            F                                                    )                                                                                      )                                                  -                s                            )                                                          cos              ⁢                              xe2x80x83                            ⁢                              (                α                )                                      -                          (                                                                    1                    -                                                                  (                                                                              n                            ⁢                                                          λ                              p                                                                                -                                                      sin                            ⁢                                                          xe2x80x83                                                        ⁢                                                          (                                                              ρ                                +                                                                  arctan                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      (                                                                          x                                      F                                                                        )                                                                                                                              )                                                                                                      )                                            2                                                                                                            n                    ⁢                                          λ                      p                                                        -                                      sin                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              ρ                        +                                                  arctan                          ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                          x                              F                                                        )                                                                                              )                                                                                  )                        -                          sin              ⁢                              xe2x80x83                            ⁢                              (                α                )                                                                        (        1        )            
In relation to FIG. 1 and Equation (1), a laser 110 transmits monochromatic light to a target 150 along a line of illumination 115. The target 150 redirects said light to a diffraction grating 120, and the diffraction grating 120 diffracts said light into a diffraction pattern. The diffraction pattern is passed through a lens 140 of a camera 130 and is recorded on a focal plane of the camera 130. Other parameters appearing in FIG. 1 and Equation (1) are as follows:
D 100 is the range along the line of illumination 115 from the target 150 to the diffraction grating 120.
d 101 is the distance from the lens 140 to the diffraction grating 120.
s 102 is the distance from the lens 140 to the line 117, wherein the line 117 is normal to grating plane of the grating 120 and passes through the intersection 118 of the illumination ray 115 with the grating plane.
n is an integer denoting the diffraction order (n=0 denotes zero-order diffraction, while n greater than 0 and n less than 0 denotes high order diffraction)
xcex is the wavelength of the light transmitted by the laser 110.
p is the pitch of the grating 120.
F 103 is the focal length of the lens 140.
x 104 is the position on the focal plane where the diffraction image forms.
xcex1 105 is the angle of a laser relative the line 117.
xcfx81 106 is the angle of the baseline of the camera 130 relative to the line 117.
An example of the related art is shown in FIG. 2. A step block 230 is a target that is illuminated by a laser 210. The laser 210 produces a sheet of monochromatic light 220. On the target 230 surface, the sheet of light 220 is diffused as wave fronts 222 back toward a diffraction grating 240. Examples of diffused light rays are shown as 224 and 225. The light diffused from the target 230 strikes the grating 240 which is in the field-of-view of a monochrome camera 250 with array sensor 255. Examples of diffracted rays are shown as extensions of rays 224 and 225. If the camera signal is viewed on a television monitor 255, it will show points 257 of horizontal displacement across the screen proportional to target range. The correlated positions on the monitor of example rays 224 and 225 are indicated.
In WO1999/044013 supra, a method is taught of varying the grating pitch p across the face of the grating so as to control the displacement x as a function of target distance D as per the embodiment of FIG. 2. A prototype embodiment of the variable pitch diffraction range finder is fully disclosed in: Tom Ditto and Douglas A. Lyon, xe2x80x9cMoly a prototype handheld three-dimensional digitizer with diffraction optics,xe2x80x9d Optical Engineering, January 2000, Vol. 39 No. 1, pp. 68-78.
In all of these prior disclosures describing diffraction range finders, the measured variable has been the displacement of a monochromatic higher-order diffraction image as a function of target range. The related as disclosed supra herein, has several drawbacks.
One drawback is the rate of acquisition. Receivers used in diffraction profilometry instruments measure relative displacements on a camera focal plane between a zero-order image and higher-order images, but the region between diffraction orders contains no illumination. A raster order scan through the dark pixels that occupy space between the sparsely distributed illuminated pixels can account for up to 99% of scan time. The diffraction range finder profilometer reported by the inventor to the National Science Foundation (DMI-9420321) has a theoretical maximum acquisition rate of 15 thousand points a second. This compares poorly with contemporary two-dimensional video cameras that routinely capture 15 million points per second.
A second limitation in the prior art of diffraction range finders is the accuracy of the acquired data. Typical receivers used in prototype diffraction range finders, such as video cameras, have less than 10 bits of resolution of spatial resolution. Even the most expensive grades of two-dimensional video cameras achieve less than 12 bits of spatial resolution in any one dimension. These limits in accuracy are then imposed on the diffraction range finder""s measurements of distance.
Another weakness in diffraction range finders of the related art is that those range finders made with plane gratings of fixed grating pitch suffer loss of resolution with target distance. Just as perspective foreshortening makes objects appear shorter as they recede into the distance, so the higher-order diffraction images made with plane gratings shift less on the focal plane as the measured range increases. There is an inverse square loss of resolution with distance.
Another difficulty in diffraction range finder manufacture is the considerable size of the grating, which contributes to the competitive cost of the instrument while adversely affecting instrument size and thereby user convenience.
An additional problem in prior diffraction range finders design is the use of a laser as the source of structured illumination. Coherent laser radiation can be a hazard to the eye and is strictly regulated by governments. Incoherent light does not pose this problem.
Thus, there is a need for a range finder that overcomes the limitations described above.
A first objective of the present invention is to make diffraction range finders that work under polychromatic incoherent illumination.
A second object of the present invention to increase the rate of acquisition of diffraction range finder.
A third object of the present invention is to minimize the occlusion liability of the range finder.
A fourth object of the present invention to provide structured illumination from a source that presents no hazard to the eye.
A fifth object of the present invention is to improve the accuracy of a diffraction range finder; and furthermore to overcome an inverse square relationship of resolution to accuracy.
A sixth object of the present invention to lower the cost of a diffraction range finder.
A seventh object of the present invention is to miniaturize the instrument.
Objectives and advantages of the present invention have been set forth in part above and will be obvious in part from, or learned by practice with, the invention. The invention consists in the parts, constructions, embodiments and combinations, herein shown and described, or as may be inferred by reading this document.
The present invention provides a method for determining range by correlating a relationship between one or more distances of a diffraction grating from an illuminated target surface with variations in the respective wavelengths of high order diffraction spectra as observed through said grating, said high order diffraction spectra being derived from broadband radiation transmitted from said illuminated target surface.
The present invention overcomes the limitations of the related art described supra.